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 81. Commutative Algebra & Algebraic Geometry http://www.math.ukans.edu/caag/

82. Commutative Algebra
commutative algebra. We will do some serious commutative algebra in this chapter, which will provide a powerful algebraic foundation
http://modular.fas.harvard.edu/papers/ant/html/node10.html
Next: Noetherian Rings and Modules Up: Classical Viewpoint Previous: Finitely generated abelian groups Contents Index
##### Commutative Algebra
We will do some serious commutative algebra in this chapter, which will provide a powerful algebraic foundation for understanding the more refined number-theoretic structures associated to number fields. In the first section we establish the standard properties of Noetherian rings and modules, including the Hilbert basis theorem. We also observe that finitely generated abelian groups are Noetherian -modules, which fills the gap in our proof of the structure theorem for finitely generated abelian groups. After establishing properties of Noetherian rings, we consider the rings of algebraic integers and discuss some of their properties.
Subsections

83. Math 252: Commutative Algebra And Algebraic Geometry
. This is a basic introductory......Math 252 commutative algebra and Algebraic Geometry (Spring 2004). Instructor. Leslie Saper.
Leslie Saper
##### Description
This is a basic introductory course in commutative algebra for first year mathematics graduate students. Commutative algebra forms the foundation on which algebraic geometry and algebraic number theory are built, however it is an important course for all students interested in studying geometry, topology, and mathematical physics. The text will be Atiyah and MacDonald's classic book, however students may also wish to consult the optional text by Eisenbud which expounds on the geometry more fully. Topics: Affine algebraic varieties, extension and contraction of ideals, modules of fractions (localization), primary decomposition, integral dependence, chain conditions, Noetherian rings, Dedekind domains, completions, and (if time) dimension theory.
##### Text
• (required) Introduction to Commutative Algebra , by M. F. Atiyah and I. G. MacDonald
• (optional) Commutative algebra with a view toward algebraic geometry , by David Eisenbud, Graduate Texts in Math., vol. 150, Springer-Verlag, Berlin and New York, 1995

84. Math 252: Commutative Algebra And Algebraic Geometry
. This is a basic, introductory course in commutative algebra.......Math 252 commutative algebra and Algebraic Geometry (Spring 2002). Instructor.
##### Instructor
Andreas Rosenchon
##### Description
This is a basic, introductory course in commutative algebra. Commutative algebra forms the foundation on which Algebraic Geometry and Algebraic Number Theory are built. As there is much more basic commutative algebra than can be covered in a one semester course, some selection of topics is necessary. Since Math 252 is a prerequisite for the Math 273 (Algebraic Geometry), but not for the Algebraic Number Theory course, there will be a strong bias towards classical algebraic geometry and away from number theory. A list of notions from algebraic geometry which will be covered is included below. We will restrict attention to algebraic varieties over algebraically closed fields. Mostly we will work with the category of affine varieties, although projective varieties will be touched upon.
Geometric topics
The Zariski topology on affine space, affine varieties, Noetherian topological spaces, Krull dimension, irreduciblity, polynomial maps between affine varieties, closed embeddings, dominant maps, product varieties, principal open subsets, affine algebraic groups, tori, affine toric varieties, the tangent space, finite maps, closed maps, quotients by finite group actions, constructible sets, images of polynomial maps, bounds on dimensions of intersections, the singular locus, open maps, flat maps, dimensions of fibers of polynomial maps, projective varieties, Hilbert functions, Bezout's theorem for intersection with a projective hypersurface, tangent cones, foundations of the theory of divisors on a smooth complex analytic space or variety (divisors will only be introduced in the algebraic geometry course; we just do the commutative algebra needed to get the theory going).

 85. IPM - A Workshop On Homological Methods In Commutative Algebra Institute for Studies in Theoretical Physics and Mathematics (IPM) A Workshop on Homological Methods in commutative algebra May 2531, 2002 Tehran, Iran.http://www.ipm.ac.ir/IPM/news/homological/announcement.jsp

86. 21-715 Algebra II (Commutative Algebra)
21715 Algebra II (commutative algebra). Contents Will present some of the basic facts of commutative algebra from the geometric point of view.
http://www.math.cmu.edu/~rami/comalg.html
 21-715 Algebra II (Commutative Algebra) Lecturer: Rami Grossberg Starting : Spring 1998, MWF 3:30 PM General: Contents: Will present some of the basic facts of commutative algebra from the geometric point of view. If time permits, I will discuss the theory of normed fields. Most of the course will be based on the following (very short) books: 1. M. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra 2. W. Fulton, Algebraic Curves The authors (of both books) claim that the books are based on undergraduate courses. Fulton mentions in the introduction to his book that he taught the contents of his book to graduate students in one week. Our pace will be slower than his! Prerequisites More information: Contact R. Grossberg WeH 6218 (ext. 8482); Email: Rami@ cmu.edu

87. Commutative Algebra Authors/titles Recent Submissions
commutative algebra. Authors and titles for recent submissions.
http://xxx.arxiv.cornell.edu/list/math.AC/recent
##### Authors and titles for recent submissions
• Fri, 4 Jun 2004 Fri, 28 May 2004 Thu, 27 May 2004 Tue, 25 May 2004 ... Mon, 24 May 2004
##### math.AC/0406057 abspspdfother
Title: Gorenstein projective dimension for complexes
Authors: Oana Veliche
Comments: Accepted for publication in Transactions AMS, submitted October 8, 2003
Subj-class: Commutative Algebra; Rings and Algebras
MSC-class:
##### math.AT/0405525 abspspdfother
Title:
Authors:
Andrew Baker Birgit Richter
Subj-class: Algebraic Topology; Commutative Algebra
MSC-class:
##### math.AC/0405526 abspspdfother
Title: Semi-dualizing modules and related Gorenstein homological dimensions
Authors: Henrik Holm Peter Jorgensen
Comments: 25 pages Subj-class: Commutative Algebra MSC-class:
##### math.AC/0405523 abspspdfother
Title: Cohen-Macaulay injective, projective, and flat dimension Authors: Henrik Holm Peter Jorgensen Comments: 18 pages Subj-class: Commutative Algebra MSC-class:
##### math.CV/0405491 abspspdfother
Title: La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes Authors: Martin Weimann Comments: 33 pages Subj-class: Complex Variables; Commutative Algebra

88. Advanced Example 2: Implementing A Non-commutative Algebra
Advanced example 2 implementing a noncommutative algebra. We need to understand how to simplify expressions in Yacas, and the best
http://yacas.sourceforge.net/codingchapter8.html
##### Advanced example 2: implementing a non-commutative algebra
We need to understand how to simplify expressions in Yacas, and the best way is to try writing our own algebraic expression handler. In this chapter we shall consider a simple implementation of a particular non-commutative algebra called the Heisenberg algebra. This algebra was introduced by Dirac to develop quantum field theory. We won't explain any physics here, but instead we shall to delve somewhat deeper into the workings of Yacas.
##### The problem
Suppose we want to define special symbols A(k) and B(k) that we can multiply with each other or by a number, or add to each other, but not commute with each other, i.e. A(k)*B(k)!=B(k)*A(k) . Here k is merely a label to denote that A(1) and A(2) are two different objects. (In physics, these are called "creation" and "annihilation" operators for "bosonic quantum fields".) Yacas already assumes that the usual multiplication operator " " is commutative. Rather than trying to redefine , we shall introduce a special multiplication sign " " that we shall use with the objects A(k) and B(k) ; between usual numbers this would be the same as normal multiplication. The symbols

89. CS 915y - Constructive Commutative Algebra
Previous CS 874b Advanced computer. CS 915y - Constructive commutative algebra. The course web site. next up previous Next Bibliography
http://www.csd.uwo.ca/faculty/moreno/node27.html
Next: Bibliography Up: Courses taugth in 2002-2003 Previous: CS 874b - Advanced computer
##### CS 915y - Constructive commutative algebra
The course web site
Next: Bibliography Up: Courses taugth in 2002-2003 Previous: CS 874b - Advanced computer Marc Moreno Maza

90. Special Session In Commutative Algebra And Algebraic Geometry At AMS-INDIA Meeti
Special Session in commutative algebra and Algebraic Geometry at AMSINDIA Meeting Tata Auditorium, Indian Institute of Science, Bangalore Organizers Sudhir R
http://www.math.iitb.ac.in/~jkv/conf/ams/
 Special Session in Commutative Algebra and Algebraic Geometry at AMS-INDIA Meeting Tata Auditorium, Indian Institute of Science, Bangalore Organizers: Sudhir R. Ghorpade, Hema Srinivasan and J. K. Verma December 17-20, 2003

 91. Commutative Algebra And Algebraic Geometry Seminars commutative algebra and algebraic geometry seminars.http://www.math.iitb.ac.in/~jkv/seminars/

92. Computational Commutative Algebra (and Algebraic Geometry)
Computational commutative algebra (and Algebraic Geometry). Eisenbud, ``commutative algebra with a view toward algebraic geometry , Springer GTM, 1995.
http://www2.math.uic.edu/~leykin/math531/
 Computational Commutative Algebra (and Algebraic Geometry) MATH 531 Fall 2004 Description: Advances in computing over the last couple of decades have revolutionized the area of commutative algebra and algebraic geometry, making tractable many problems inaccessible in the past, and providing powerful tools for experimentation. This course serves a dual purpose: its objective is to introduce the basic concepts of commutative algebra, as well as provide hands-on experience with computer algebra software. Besides regular lectures, there would be (either weekly or biweekly) lab sessions, where we would use Maple and Macaulay 2 to solve computational problems. Prerequisites: The course is self contained; firm knowledge of linear algebra is the only requirement. The material should be accessible for both pure math and MCS graduate students. Texts: (main) Cox, Little, O'Shea, ``Using algebraic geometry'', Springer GTM, 1998. Cox, Little, O'Shea, ``Ideals, varieties, and algorithms'', Springer UTM, 1997. Eisenbud, ``Commutative Algebra with a view toward algebraic geometry'', Springer GTM, 1995.

93. Student Commutative Algebra / Algebraic Geometry Seminar
Student commutative algebra / Algebraic Geometry Seminar. The seminar is run by students in commutative algebra and Algebraic Geometry.
http://www.math.lsa.umich.edu/~fenescu/studentseminar/
##### Fall 2000: Thursdays 4 - 5 pm, 3866 East Hall
The seminar is run by students in Commutative Algebra and Algebraic Geometry. If you would like to give a talk or to be added to the seminar mailing list, send an e-mail to fenescu@math.lsa.umich.edu
##### Schedule of Talks (Fall 2000)
Click on the title of a talk for the abstract (if available).

94. References For Commutative Algebra
References for commutative algebra. MF Atiyah, IG MacDonald Introduction to commutative algebra N. Bourbaki commutative algebra
http://www.math.metu.edu.tr/~akisisel/comalgref.htm
##### References for Commutative Algebra
M.F. Atiyah, I.G. MacDonald "Introduction to commutative algebra"
N. Bourbaki "Commutative algebra"
D. Cox, J. Little, D. O'Shea "Ideals, varieties and algorithms"
D.Eisenbud "Commutative algebra with a view towards algebraic geometry"
I. Kaplansky "Commutative rings"
E. Kunz "Introduction to algebra and algebraic geometry"
H. Matsumura "Commutative ring theory"
M. Nagata "Local Rings"
C. Peskine "An algebraic introduction to complex projective geometry"
R.P. Stanley "Combinatorics and commutative algebra" W.V. Vasconcelos "Computational methods in commutative algebra and algebraic geometry" O. Zariski, P. Samuel "Commutative Algebra"

95. Studiegids Wiskunde 2003 (Commutative Algebra)
commutative algebra. complexe-functietheorie - computational algebraic number - computational group theory - computer statistics - computeralgebra
http://www.studiegids.sci.kun.nl/ned/wiskunde_2003/vakken/1141
 Wiskunde 2003 Faculteit der Natuurwetenschappen, Wiskunde en Informatica home Universiteit Faculteit NWI Studiegidsen ... - colloquium - commutative algebra - complexe-functietheorie - computational algebraic number - computational group theory - computer statistics ... printer versie 10.0 ects docent: dr. A.R.P van den Essen speciale website: Eerste bijeenkomst: in de eerste week van het semester / kwartaal tentamen:

96. CourseÂ Catalog Wiskunde 2003 (Commutative Algebra)
commutative algebra. WM026A, 10.0 ects, lecturer What is commutative algebra about? To make this clear let s start with a kvector space V, where k is a field.
http://www.studiegids.sci.kun.nl/eng/wiskunde_2003/vakken/1141
Wiskunde 2003 Faculty of Science and Mathematics
home
University Faculty of science Course catalogs ...
- colloquium

- commutative algebra - complexe-functietheorie
- computational algebraic number

- computational group theory

- computer statistics
...
printer version
##### Commutative algebra
10.0 ects lecturer: dr. A.R.P van den Essen special website: First meeting: in the first week of the semester / quarter exam:
##### Course description
What is commutative algebra about? To make this clear let's start with a k -vector space V , where k is a field. So V is a set equipped with an addition, which makes V into an abelian group, and a scalar multiplication with scalars from k . Furthermore the classical distibutive laws hold. If we replace k by an arbitrary commutative ring R we get a so-called R -module. This notion generalises most of the notions one meets during a Bachelor's study Mathematics. For example it will turn out that a Z-module is the same as an abelian group, a k x ]-module is the same as a k -vector space together with a linear transformation and an ideal I in a ring R is an example of a so-called R -submodule of R . Also the quotient ring R/I is an R -module etc. The theory of

97. PERSEUS BOOKS GROUP - Search Results - Introduction To Commutative Algebra (On D
Introduction To commutative algebra (On Demand) by MF Atiyah, University of Oxford and IG MacDonald, University of Oxford. Paperback
http://www.perseusbooksgroup.com/perseus-cgi-bin/display/0-201-40751-5

98. Algebraic Geometry And Commutative Algebra
Seminars related to Algebraic Geometry and commutative algebra. Preprint Archives in Algebraic Geometry, commutative algebra and related fields.
http://www.science.nd.edu/math/research/algebra_geom/index.shtml
 Math Faculty Mario Borelli Eimear Byrne Karen Chandler Alan Howard ... Andrew Sommese Graduate Students Student Advisor Daniel Bates Sommese Elisa Gorla Migliore Guangyue Han Rosenthal Ryan Hutchinson Rosenthal Carmelo Interlando Rosenthal Christine Kelley Rosenthal Seminars related to Algebraic Geometry and Commutative Algebra All seminars listed are in Hayes-Healy Hall . It is number 88 on the campus map . Just click on the 6th grid on the smaller map to see the building number. Algebraic Geometry and Commutative Algebra Seminar every Tuesday, Time: 9:00-10:00 am, 129 Hayes-Healy Hall To see the schedule of talks in these or any other seminar or colloquium at Notre Dame, go to the " Mathematics Colloquia and Seminars page " on the Math Department Home Page Preprint Archives in Algebraic Geometry, Commutative Algebra and related fields Here is a link to the Mathematics E-Print Archives at Duke/MSRI/SISSA . It has a lot of useful information and links. Its archives include Places of Interest on the Web

99. Commutative Algebra
next up previous Next Multivariate Polynomial Rings Up V2.9 Features Previous Algebraically Closed Fields commutative algebra.
http://magma.maths.usyd.edu.au/magma/Features/node132.html
Next: Multivariate Polynomial Rings Up: V2.9 Features Previous: Algebraically Closed Fields
##### Commutative Algebra
The Magma facility for commutative rings allows the user to define any ring, starting from the ring of integers, by repeatedly applying the four basic constructions: transcendental extension quotient by an ideal localization , and completion . Rings derived from a polynomial ring will be considered in this section, while fields, their orders and valuation rings will be presented in the following section. The following rings and modules are considered here:
• Multivariate polynomial rings
• Ideal theory of multivariate polynomial rings
• Affine algebras
• Modules over affine algebras

The basic computational problems for commutative rings include:
• A canonical form for elements
• Efficient arithmetic
• A canonical representation (i.e., standard basis) for ideals
• Arithmetic with ideals
• Formation of quotient rings
• Ideal decomposition, i.e., primary decomposition
• The study of modules over rings
The fundamental tools on which most machinery for computational (commutative) ring theory is based include factorization of elements in a UFD, the efficient construction of standard bases for ideals and the factorization of ideals.

100. Commutative Algebra
next up previous Next Ideal Theory and GrÃ¶bner Up No Title Previous Local (including padic) Rings commutative algebra. Ideal
http://magma.maths.usyd.edu.au/magma/ReleaseNotes/rel28/node39.html
Next: Up: No Title Previous: Local (including p-adic) Rings
##### Commutative Algebra

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